C.V.

Education

• Graduate: University of Pennsylvania, Ph.D., 1991

• Undergraduate: University of Pennsylvania, B.S., 1986

Academic Appointments

• 9/03 - Present: Professor, Loyola University Chicago

• 9/98 - 8/03: Associate Professor, Loyola University Chicago

• 9/97 - 5/98: Visiting Associate Professor: Texas A&M University

• 9/97 - 8/98: Associate Professor, Mississippi State University

• 9/95 - 8/97: Assistant Professor, Mississippi State University

• 9/91 - 8/95: Postdoctoral Assistant Professor: University of Michigan

Publications

• Most publications are available on arxiv 

• An explicit deformation formula with noncommuting derivations, Ring theory (Ramat Gan and Jerusalem, 1988/1989), 396–403, Israel Math. Conf. Proc., 1, Weizmann, Jerusalem, 1989.  (With V. Coll and M. Gerstenhaber)

• Separable functors revisited. Comm. Algebra 18 (1990), no. 5, 1445–1459. (With F. Van Oystaeyen)

• Quantization of tensor representations and deformation of matrix bialgebras. J. Pure Appl. Algebra 79 (1992), no. 2, 169–190.

• Quantum symmetry. Quantum groups (Leningrad, 1990), 9–46, Lecture Notes in Math., 1510, Springer, Berlin, 1992. (With M. Gerstenhaber and S.D. Schack)

• Quantum groups, cohomology, and preferred deformations. Proceedings of the XXth International Conference on Differential Geometric Methods in Theoretical Physics, Vol. 1, 2 (New York, 1991), 529–538, World Sci. Publ., River Edge, NJ, 1992.  (With M. Gerstenhaber and S.D. Schack)

• Construction of quantum groups from Belavin-Drinfelʹd infinitesimals. Quantum deformations of algebras and their representations (Ramat-Gan, 1991/1992; Rehovot, 1991/1992), 45–64, Israel Math. Conf. Proc., 7, Bar-Ilan Univ., Ramat Gan, 1993.  (With M. Gerstenhaber and S.D. Schack)

• Quantum Weyl algebras. J. Algebra 176 (1995), no. 3, 861–881. (With J.J. Zhang)

• Boundary solutions of the classical Yang-Baxter equation. Lett. Math. Phys. 40 (1997), no. 4, 337–353. (With M. Gerstenhaber)

• Nonstandard solutions of the Yang-Baxter equation. Lett. Math. Phys. 44 (1998), no. 1, 67–75. (With T. J. Hodges).

• Bialgebra actions, twists, and universal deformation formulas. J. Pure Appl. Algebra 128 (1998), no. 2, 133–151. (With J.J. Zhang)

• Boundary solutions of the quantum Yang-Baxter equation and solutions in three dimensions. Lett. Math. Phys. 44 (1998), no. 2, 131–141. (With M. Gerstenhaber)

• Compatible deformations. Trends in the representation theory of finite-dimensional algebras (Seattle, WA, 1997), 159–168, Contemp. Math., 229, Amer. Math. Soc., Providence, RI, 1998. (With M. Gerstenhaber)

• Generators and relations for Schur algebras. Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 54–62 (electronic). (With S. Doty)

• The Donald-Flanigan problem for finite reflection groups. EuroConférence Moshé Flato 2000, Part I (Dijon). Lett. Math. Phys. 56 (2001), no. 1, 41–72. (With M. Gerstenhaber and M. Schaps)

• Presenting Schur algebras. Int. Math. Res. Not. 2002, no. 36, 1907–1944. (With S. Doty)

  • Algebraic deformations arising from orbifolds with discrete torsion. J. Pure Appl. Algebra 187 (2004), no. 1-3, 51–70. (With A.  Căldăraru and S. Witherspoon)

• Presenting Schur algebras as quotients of the universal enveloping algebra of gl(2). Algebr. Represent. Theory 7 (2004), no. 1, 1–17. (With S. Doty)

• Quantum groups and deformation quantization: explicit approaches and implicit aspects. J. Math. Phys. 45 (2004), no. 10, 3703–3741. (With P. Bonneau, M. Gerstenhaber and D. Sternheimer)

• Diagrams of Lie algebras. J. Pure Appl. Algebra 196 (2005), no. 2-3, 169–184. (With M. Gerstenhaber and S.D. Schack)

• Presenting generalized Schur algebras in types B, C, and D. Adv. Math. 206 (2006), no. 2, 434–454. (With S. Doty and J. Sullivan)

• On the defining relations for generalized q-Schur algebras. Adv. Math. 221 (2009), no. 3, 955–982. (With S. Doty and J. Sullivan)

• The principal element of a Frobenius Lie algebra. Lett. Math. Phys. 88 (2009), no. 1-3, 333–341.

• Topics in algebraic deformation theory. Higher Structures in Geometry and Physics,  1-24, Progress in Mathematics 287, Springer, New York, 2010.

• Meander graphs and Frobenius seaweed algebras (with V. Coll and C. Magnant), Journal of Generalized Lie Theory, 5, (2011), 1 - 7 (With V. Coll and C. Magnant).

• On the cohomology of the Weyl algebra, the quantum plane, and the q-Weyl algebra, Journal of Pure and Applied algebra 218 (2014), 879-887. (With M. Gerstenhaber)

• Deformations associated with rigid algebras, Journal of Homotopy and Related Structures (2014), in press.

• Cellular bases of generalized q-Schur algebras(with S. Doty, Mathematical Proceedings of the Cambridge Philosophical Society, 162, (2017), 533-560. 

• The Collaborative Development of Active Learning at Loyola University Chicago as Part of the SEMINAL Network, PRIMUS 31, no 3-5 (2021), 281- 295. 

• Peter-Weyl bases, preferred deformations and Schur-Weyl duality (with A. Gillman and P. Tingley), Representation Theory, Mathematical Physics, and Integrable Systems, Progress in Mathematics 340, https://doi.org/10.1007/978-3-030-78148-4_9. 

• Schur-Weyl Duality for Tensor Powers of the Burau Representation (with S. Doty), Res Math Sci 8, 47 (2021). https://doi.org/10.1007/s40687-021-00282-3. 

• Schur-Weyl Duality for Twin Groups (with S. Doty), Transformation Groups (2022). https://doi.org/10.1007/s00031-022- 09708-w 

• The Partial Temperley-Lieb Algebra and its Representations (with S. Doty), Journal of Combinatorial Algebra,  (7), 2023, no. 3/4, pp 401-439. 

• An orthogonal realization of representations of the Temperley–Lieb algebra  (with S. Doty), Journal of Algebra, (655), 2024, no. 1, pp 394-432.

• Origins of the Temperley-Lieb Algebra: Early History, preprint,  (with S. Doty) , arXiv:2307.11929, 2023. 

Edited Books

• Higher Structures in Geometry and Physics, Progress in Mathematics 287, Springer, New York, 2010. xv+362pp. (A. Cattaneo, A. Giaquinto, and P. Xu, eds.)